Mathhammer: Scatter dice probability

“Our bombs are smarter than the average high school student. At least they can find Kuwait.” - A. Whitney Brown

A few days ago I started to think of an easy formula people could use for figuring out the probability that a blast weapon would scatter within a certain distance. Here is what I came up with.

How the scatter dice work
- You roll 1D6 in which two sides have a [hit] marker and four sides have an [arrow] for the direction the blast template scatters.
- You roll 2D6 and add the numbers together to see how far the blast template scatters if an [arrow] is rolled.
- Sometimes you can subtract the BS of the shooter from the 2D6 roll.

Here is what we know
- 1 out of 3 times the template doesn't scatter at all due to the [hit] marker.
- 2 out of 3 times the template doesn't scatter if the 2D6 roll is less than or equal to your BS.

So far the formula looks like this
- P=Probability that blast templates won't scatter
- P = ( 1/3 ) + ( chance that 2D6 - BS = 0 )
- the ( 1 / 3 ) is because one out of three times we roll a [hit] on the scatter dice

How do you figure out the odds of a 2D6 roll?
- There are 36 (6*6) different possibilities when rolling 2D6
- Here is a chart that shows how many possibilities there are for each result on a 2D6 Roll

2D6 ROLL --- # Possibilities
2 --- 1
3 --- 2
4 --- 3
5 --- 4
6 --- 5
7 --- 6
8 --- 5
9 --- 4
10 --- 3
11 --- 2
12 --- 1


Now what does the formula look like?
- P=Probability that blast templates won't scatter
- POSS=Number of possibilities 2D6 will be equal to or less than your BS
- P = ( 1/3 ) + ( ( POSS / 36 ) * 2/3 )

Let's go through some examples

What is the probability that a blast template won't scatter, with a BS 4 shooter?
- There are 6 ways to roll a 4 or less on 2D6, 1 way to roll 2, 2 ways to roll 3, and 3 ways to roll 4.
- So plug in the values and you get
P = ( 1/3 ) + ( ( 6/36 ) * 2/3 ) = 0.44 = 44% chance the template won't scatter

What is the probability that a blast template will scatter 2 inches or less with a BS 3 shooter?
- A BS 3 shooter needs to roll a 5 or less on 2D6 to scatter 2 inches or less.
- Thee are 10 ways to roll 5 or less on 2D6, 1 way to roll 2, 2 ways to roll 3, 3 ways to roll 4, and 4 ways to roll 5.
- So plug in the values and you get
P = ( 1/3 ) + ( (10/36) * 2/3 ) = 0.518 = 52% chance the template won't scatter more than 2 inches

What is the probability that my deep striking Necron lord will scatter 8 inches or less?
- You need to roll 8 or less on 2D6 to scatter 8 inches or less.
- There are 26 ways to roll 8 or less on 2D6.
- So plug in the values and you get
P = ( 1/3 ) + ( (26/36) * 2/3 ) = 0.814 = 81% chance of not deep striking more than 8 inches

- I hope this helps everyone, and of course probability for blast template scatter will be in FarseerMobile and FarseerOnline when they are released. Let me know what you think!